This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein–Gordon equations, KdV equations as well as Navier–Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.
This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.
Sample Chapter(s)
Chapter 1: Fourier multiplier,function space Xsp,q (371 KB)
Contents:
- Fourier Multiplier, Function Spaces Xsp,q
- Navier–Stokes Equation
- Strichartz Estimates for Linear Dispersive Equations
- Local and Global Wellposedness for Nonlinear Dispersive Equations
- The Low Regularity Theory for the Nonlinear Dispersive Equations
- Frequency-Uniform Decomposition Techniques
- Conservations, Morawetz' Estimates of Nonlinear Schrödinger Equations
- Boltzmann Equation without Angular Cutoff
Readership: Graduate students and researchers interested in analysis and PDE.
